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VOL. 28 | 2000 Length Functions for $G(r, p, n)$
Toshiaki Shoji

Editor(s) Kazuhiko Koike, Masaki Kashiwara, Soichi Okada, Itaru Terada, Hiro-Fumi Yamada

Abstract

In this paper, we construct a length function $n(w)$ for the complex reflection group $W = G(r, p, n)$ by making use of certain partitions of the root system associated to $\widetilde{W} = G(r, 1, n)$. We show that the function $n(w)$ yields the Poincaré polynomial $P_W(q)$. We give some characterization of this function in a way independent of the choice of the root system.

Information

Published: 1 January 2000
First available in Project Euclid: 20 August 2018

zbMATH: 0986.20039
MathSciNet: MR1864487

Digital Object Identifier: 10.2969/aspm/02810327

Rights: Copyright © 2000 Mathematical Society of Japan

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